Context free grammar for a language

Question

How would I go about writing a context free grammar for the following language:

{a^x b^y c^z | x >= 0, y >= 0, z >= 0, y = x + z}

Answer 1

Note that

b^y = b^(x+z) = b^x b^z

So you can rewrite the specification as:

a^x b^x b^z c^z

Let L = a^x b^x, x >= 0, and R = b^z c^z, z >= 0

I think you should be able to fill in the rest from there...